Tabular data have been playing a vital role in diverse real-world fields, including healthcare, finance, etc. With the recent success of Large Language Models (LLMs), early explorations of extending LLMs to the domain of tabular data have been developed. Most of these LLM-based methods typically first serialize tabular data into natural language descriptions, and then tune LLMs or directly infer on these serialized data. However, these methods suffer from two key inherent issues: (i) data perspective: existing data serialization methods lack universal applicability for structured tabular data, and may pose privacy risks through direct textual exposure, and (ii) model perspective: LLM fine-tuning methods struggle with tabular data, and in-context learning scalability is bottle-necked by input length constraints (suitable for few-shot learning). This work explores a novel direction of integrating LLMs into tabular data through logical decision tree rules as intermediaries, proposing a decision tree enhancer with LLM-derived rule for tabular prediction, DeLTa. The proposed DeLTa avoids tabular data serialization, and can be applied to full data learning setting without LLM fine-tuning. Specifically, we leverage the reasoning ability of LLMs to redesign an improved rule given a set of decision tree rules. Furthermore, we provide a calibration method for original decision trees via new generated rule by LLM, which approximates the error correction vector to steer the original decision tree predictions in the direction of "errors" reducing. Finally, extensive experiments on diverse tabular benchmarks show that our method achieves state-of-the-art performance.

Algorithm configuration, which involves selecting algorithm parameters based on sampled problem instances, is a crucial step in applying modern algorithms such as SAT solvers. Although prior work has attempted to understand the theoretical foundations of algorithm configuration, we still lack a comprehensive understanding of why practical algorithm configurators exhibit strong generalization performances in real-world scenarios. In this paper, through the lens of machine learning theory, we provide an algorithm-dependent generalization bound for the widely used model-based algorithm configurators under mild assumptions. Our approach is based on the algorithmic stability framework for generalization bounds. To the best of our knowledge, this is the first generalization bound that applies to a model closely approximating practical model-based algorithm configurators.

Gradient boosting is widely popular due to its flexibility and predictive accuracy. However, statistical inference and uncertainty quantification for gradient boosting remain challenging and under-explored. We propose a unified framework for statistical inference in gradient boosting regression. Our framework integrates dropout or parallel training with a recently proposed regularization procedure called Boulevard that allows for a central limit theorem (CLT) for boosting. With these enhancements, we surprisingly find that increasing the dropout rate and the number of trees grown in parallel at each iteration substantially enhances signal recovery and overall performance. Our resulting algorithms enjoy similar CLTs, which we use to construct built-in confidence intervals, prediction intervals, and rigorous hypothesis tests for assessing variable importance in only O(nd2) time with the Nystr om method. Numerical experiments verify the asymptotic normality and demonstrate that our algorithms perform well, do not require early stopping, interpolate between regularized boosting and random forests, and confirm the validity of their built-in statistical inference procedures.

The advent of Machine Learning as a Service (MLaaS) has heightened the trade-off between model explainability and security.

CART random forests are among the most widely used modern predictive methods, with well-documented empirical success. Yet, at the mechanistic level, the algorithm is often treated as a black box because of its complexity. In this paper, we develop a stochastic-control perspective on feature-subsampled CART random forests, named CART random opportunity-set allocation (CART-ROSA). At each node, the random subset of features is interpreted as a random feasible action set, and the CART split rule as a masked-action allocation policy. This policy induces a controlled stochastic process over informative split-count states, whose terminal law determines both single-tree error and cross-tree interaction terms in the forest mean squared error (MSE). Such representation opens the black box of CART-forests by separating two design levers: the informative-opportunity rate induced by feature subsampling, and the contraction strength from the within-mask split policy. We establish that the CART policy is locally stabilizing: it contracts imbalances in informative split allocations and concentrates terminal tree geometry. At the system level, however, it can be globally suboptimal for the forest objective. Specializing to the linear model, we derive the MSE risk expansion explicitly. Our results show how an operations-research perspective makes tractable a theoretical gap difficult to access from the standard algorithmic description of CART forests.

We develop a rigorous statistical theory of multi-head attention (MHA) as an ensemble of Nadaraya-Watson (NW) kernel regression estimators. Building on the algebraic identity between single-head softmax attention and the NW estimator, we prove that MHA is a structured ensemble of H NW estimators, each operating in a distinct learned projection subspace of the key space. We derive an explicit Bias-Variance-Covariance decomposition of the MHA mean squared error, showing that variance reduction depends not merely on the number of heads H but fundamentally on the decorrelation of head outputs. Decorrelation is governed by the principal angles between learned projection subspaces: orthogonal projections yield maximum variance reduction; aligned projections yield none. We introduce the Head Diversity Index (HDI), a computable spectral measure of inter-head decorrelation, and prove that MHA mean squared error is monotonically decreasing in HDI. This provides the first rigorous theoretical explanation for the empirically observed specialization of attention heads. Under a fixed total-dimension budget D = H * d_k, we solve the optimal head-dimension allocation problem, deriving the MSE-minimizing pair (H*, d_k*) from data distribution and regression smoothness. The solution yields a new architectural scaling law: the optimal per-head dimension grows logarithmically with training set size, while the optimal number of heads grows nearly linearly with the total budget D. Our framework unifies three strands of prior work: the NW theory of single-head attention, the general weighting theory for ensemble learning, and the decorrelation-variance-reduction isomorphism between biological and computational ensembles. Multi-head attention is the Transformer's instantiation of a universal principle: identical agents plus diversity-enforcing mechanisms yields emergent optimality.

One of the most fundamental properties of a machine learning model is its complexity, with applications across topics such as interpretation, generalization, and model selection. Despite its importance, there is no canonical, model-agnostic way to assess a model's complexity. While simple heuristics, such as the number or magnitude of parameters, yield very crude estimates, hyperparameter-based approaches, such as polynomial degree or kernel length scale, do not generalize across model classes. More rigorous methods, including the Vapnik-Chervonenkis dimension (VCD) (Vapnik, 2013), Rademacher complexity (RMC) (Bartlett and Mendelson, 2002), and effective number of parameters (or effective degrees of freedom, ENP) (Efron, 1986), are difficult, or even impossible, to compute in practice, leaving the user to resort to crude bounds and/or approximations. The topic is further complicated by the often overlooked distinction between model and function complexity, where the former sets a ceiling on the latter.

Tree ensembles such as random forests (RFs) and gradient boosting machines (GBMs) are among the most widely used supervised learners, yet their theoretical properties remain incompletely understood. We adopt a spectral perspective on these algorithms, with two main contributions. First, we derive minimax-optimal convergence for RF regression, showing that, under mild regularity conditions on tree growth, the eigenvalue decay of the induced kernel operator governs the statistical rate. Second, we exploit this spectral viewpoint to develop compression schemes for tree ensembles. For RFs, leading eigenfunctions of the kernel operator capture the dominant predictive directions; for GBMs, leading singular vectors of the smoother matrix play an analogous role. Learning nonlinear maps for these spectral representations yields distilled models that are orders of magnitude smaller than the originals while maintaining competitive predictive performance. Our methods compare favorably to state of the art algorithms for forest pruning and rule extraction, with applications to resource constrained computing.